For exchanging or storing data, a sequence of bits is represented by a physical quantity, such as an electromagnetic wave for wireless exchange and a flux density pattern for storage on a magnetic disc or tape drive. The bits are encoded into the physical quantity according to a modulation scheme. The physical quantity is also referred to as a modulation symbol. The encoding according to the modulation scheme is also referred to as keying. Quadrature Phase-Shift Keying (QPSK) is an example for a modulation scheme applied for wireless exchange. Run-Length Limited (RLL) coding is an example for a line modulation scheme used in both telecommunications and storage systems.
The modulation scheme assigns one modulation symbol to a sequence of two or more bits. The modulation symbol may thus assume four or more different values, e.g., to improve an effective data rate by exploiting the continuity of the physical quantity. The different values are collectively referred to as a symbol alphabet. Furthermore, encoding a plurality of bits into one modulation symbol allows representing the data as a sequence of changes in the physical quantity for edge detection or Partial Response Maximum Likelihood (PRML) interpretation of the sequence.
The symbol alphabet specifies ideal symbols, each of which represents a certain bit sequence. A modulation symbol received on a noisy channel does not necessarily coincide uniquely with one of the symbols of the symbol alphabet. Given the received modulation symbol, it is possible to provide likelihood values for different transmit hypotheses, i.e., for the different symbols of the symbol alphabet.
For assessing the reliability of an individual bit out of the bit sequence, it is necessary to take into account the likelihood values of all possible transmit hypotheses, since the likelihood of each transmit hypothesis contributes to the likelihood for the individual bit being either 0 or 1. The reliability of the individual bit can be represented by a so-called Log-Likelihood-Ratio (LLR). In implementations of both telecommunications and storage systems, the LLRs of individual bits are input to a channel decoder.
Document EP 2 346 223 A1 describes a conventional technique for calculating LLRs received on a Single Input Single Output (SISO) channel. Research publication “Efficient Soft Demodulation in MIMO-OFDM Systems with BICM and Constant Modulus Alphabets” by D. Seethaler et al., Proc. IEEE ICASSP 2006, pp. 105 to 108, suggests an approximation for reducing the complexity of computing LLRs for bits received on a Multiple Input Multiple Output (MIMO) channel.
For a sequence including 3 bits, the symbol alphabet comprises at least 2J symbols so that the likelihood values of 2J symbol hypotheses have to be taken into account for computing the reliability of one bit. For a 4×4 MIMO channel with Quadrature Amplitude Modulation (QAM) of order 64 (i.e., 64-QAM), more than 400,000,000 likelihood values have to be combined. As a consequence, conventional approaches for assessing bit reliability are computationally complex in at least some situations and can become infeasible for practical systems, e.g., mobile devices.